Problem 5.7 Projection of Planes – A square lamina of side 80 mm rests on a corner on H.P. and it is inclined with H.P. such that its plan is a rhombus with a diagonal of 40 mm. The long diagonal is inclined with the V.P. at 45°. Determine its inclination with H.P. and draw it’s projections.
Step-1 Draw a horizontal x-y line of some suitable length.
Step-2 Draw a square of side 80 mm below the x-y line at some suitable distance as shown into the figure such that it’s all the sides should be at an angle 45° with the x-y line. And give the notations. It is the top view of the 1st stage.
Step-3 From the notations of the square, draw vertical projectors up to the x-y line, from these points of intersections, draw a medium dark horizontal line, and give the notations as shown into the figure. It is the front view of the 1st stage.
Step-4 From the top view of the 1st stage, draw horizontal projectors from all the points in right hand side direction. From theses projectors, mark point a & c at the distance equal to 40 mm from each other. And connect all the points in sequence with medium dark straight lines as shown in the figure. Its shape is a rhombus. It is top view of the 2nd stage.
Step-5 Mark a point a’ on the x-y line on the projector from the point a of the top view of the 2nd stage. With a’ as center and radius equal to the distance a’-c’ in the front view of the 1st stage cut, the vertical projector coming in upward direction from the point c of the top view of the 2nd stage. And draw a medium dark line between these points a’ & c’. And give the other notations on it. It is the front view of the 2nd stage.
Step-6 Copy the top view of the 2nd stage at an angle 45°, such that its diagonal b-d should make the angle with the x-y line as show into the figure, with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.
Step-7 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.
Step-8 From these respective points of intersections, draw medium dark line from the all points in sequence, and give the notations. It is the front view of the 3rd stage.
Step-9 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.